Using Client Object Model in RESTful web service deployed to subfolder of ISAPI (_vti_bin) - change user context

Does anybody have a link to an article or a code snippet to get the correct user context (instead of IUSR or app pool account, which is what you get) when using the Client Object Model in a custom web service deployed to a subfolder of ISAPI (_vti_bin) in SharePoint 2013?  

I know that I can use the server object model and that works great.  That's not what I want to do.  I want this to be portable and use the Client Object Model.

Thanks!

Regards,

Mike H.